Having recently played them, i thought i'd post my thoughts. I'm playing the BTS version with BTS patch 3.03 and no Rhye's updates. Game was played on Monarch.
(1) UHV #1: Conquer China by 1300. Now, that's really fast, and i'm not totally clear on what is meant by china. But i took a deep breath, cried as i threw keshiks at beijing, and steamrolled china fast enough.
Notes: A - The version i'm playing doesn't display year. Instead it gives Time Period Turn #. (So Medieval Turn 211, and so forth). This is really annoying if your goal is to accomplish X feat by year Y since you have no idea how close you are to that year, and thus no idea how many turns you have.
B - The "sacking cities causes others to surrender to you" doesn't seem to be implemented very well. I sacked the city immediately south of me, and the Chinese city NE of Beijing almost immediately surrendered to me. So far so good. I then sack Beijing and raze it to the ground, and no cities surrender to me, even as i go marauding down the coast. (They've all become independent, because i nailed the Chinese capitol, but you'd think this would make them more likely to bow to their new mongol masters). Razing a further city of the newly independent Chinese states similarly accomplishes nothing. I'm annoyed, both because i didn't keep those cities, and because my power seems to be accomplishing nothing.
Working my way south, i raze the first Khmer city - no other Khmer cities join me. I take teh capitol (they rebase farther south), raze another city (they have two left even after that) and still no cities join me. My Keshiks are racing towards them the entire time (in part because i have no clue what year it is, and so that 12% thing is pretty scary when you're at 4%.)
(Later, i'll make use of my power one more time by razing an arabian city which forces the capitulation of one of their other cities. Razing further arabian cities accomplished nothing. Two uses of my power all game isn't very exciting).
(2) UHV #2: Raze 7 cities. Trivial. No comment needed.
(3) UHV #3: Control 12% land area by 1500... oh dear god.
So, i rampage through china and khmer, capture tibet (Lhasa), and then rush units across the desert north of the himalayas (Gobi?) to reach additional cities. I also start spamming settlers in my northernmost cities to populate Siberia. The rest of my cities are spamming Keshiks to provide military units, I turn the two Great Generals i've produced into super-units to aid the conquest, and my workers complete the golden road (unfinished as of my start) to speed their journey. I grab Samarkand and some other nearby cities, run down into the independent indian territories (mostly to stop their massive culture from infringing on my cultural boundaries way over in china/tibet!), and then provoke a war with the arabs. I've basically covered the mongolian historical extent at this point and am sitting at around 9.5% land area. Raze an arab city, have another arab city come over to me, push past 10%, and suddenly my stability goes bad (it had been neutral to good all game previously). And i'm thinking "crap, i've exceeded my historical boundaries". But i've razed a second arab city, so i figure i'm owed a few more free conversions (massive keshik pushes can be disturbingly fast). I advance on arab cities in 3 directions - no conversions (the heck!?). And then the next turn my empire collapses (yep, 2 turns of showing unstable and then boom, collapse). A few turns later i get a "hi, we're around" greet from a bunch of european civs, and i figure 1500 is upon me. My "control 12% has gone from Not Yet to NO.
So yeah, 12% is just crazy talk. In part, because the mongolian special doesn't seem to be working (which eats valuable time during which your cities could be building stuff while they revolt after conquest, because you had to take them instead of razing one and gaining one or two ready to work immediately). If the mongolian special actually worked as advertised, it'd be remarkably more plausible. A second problem is the massive culture of Indian subcontinent cities, which eat into your cultural radii - especially that one city which you can't get to because all land routes to it are blocked by jungle... i forget the name - its short and begins with P. But finally, 12% seems to be bigger than the historical mongolian empire ever got, and i just collapsed as soon as i started pushing seriously beyond their historical borders. And really, i was beyond in a number of places, including SE Asia, N India, and the Arabian peninsula.
Having watched my empire degenerate in civil war, i quit shortly thereafter. It would have been fun to win immediately before that happened (and highly historical too), but 12% was just too much for me.
Ok, i didn't even try for japan. I know how well that worked historically, and building boats seemed counterproductive when what i really needed was mounted units asap in unlimited quantities. I did build some culture buildings for cultural expansion at one point in a few cities - and ran no state religion so i could get the +culture from every religion in my empire. I doubt investment in more culture would have actually helped me claim significantly more territory. The places that really needed it were all relatively recently captured, and there wouldn't have been time to build cultural buildings to pop the borders fast enough after they came out of revolt.
If i hadn't collapsed, and my racial power had worked as advertised, i figure the arabian cities +2 more turns of rapid conquest could have given me 12%. I had the Keshiks to do it (about 15 in the region of the arabian peninsula).
Oh well, i briefly held all of asia. I suppose the Khans didn't do any better - heck, i got as far as the Red Sea and they never did. But basically, this was me taking a lot of time to say that 'yes, the Mongol UHV #3 is totally unreasonable if you try to play it out historically'. I think i noticed someone else saying they did it by going to the Americas... i don't even want to know where they got the tech for that. I just stopped researching to pay for my empire at some point. (Speaking of which - all the civics choices that straight-out give stability benefits aren't even an option for mongolia going for UHVs... those techs require too many flasks to even think about).